Derivative function：
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Current location：Derivative function > Derivative function calculation history > Answer
There are 7 questions in this calculation: for each question, the 4 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/7]Find\ the\ 4th\ derivative\ of\ function\ \frac{x}{}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[2/7]Find\ the\ 4th\ derivative\ of\ function\ xsqrt(-1)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( xsqrt(-1)\right)}{dx}\\=&sqrt(-1) + x*0*\frac{1}{2}*-1^{\frac{1}{2}}\\=&sqrt(-1)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( sqrt(-1)\right)}{dx}\\=&0*\frac{1}{2}*-1^{\frac{1}{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[3/7]Find\ the\ 4th\ derivative\ of\ function\ xln(0)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( xln(0)\right)}{dx}\\=&ln(0) + \frac{x*0}{(0)}\\=&ln(0)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( ln(0)\right)}{dx}\\=&\frac{0}{(0)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[4/7]Find\ the\ 4th\ derivative\ of\ function\ xtan(90)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( xtan(90)\right)}{dx}\\=&tan(90) + xsec^{2}(90)(0)\\=&tan(90)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( tan(90)\right)}{dx}\\=&sec^{2}(90)(0)\\=&0\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[5/7]Find\ the\ 4th\ derivative\ of\ function\ x{0}^{-2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{0}x\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{0}x\right)}{dx}\\=&\frac{1}{0}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{1}{0}\right)}{dx}\\=&0\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[6/7]Find\ the\ 4th\ derivative\ of\ function\ xarcsin(2)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( xarcsin(2)\right)}{dx}\\=&arcsin(2) + x(\frac{(0)}{((1 - (2)^{2})^{\frac{1}{2}})})\\=&arcsin(2)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( arcsin(2)\right)}{dx}\\=&(\frac{(0)}{((1 - (2)^{2})^{\frac{1}{2}})})\\=&0\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[7/7]Find\ the\ 4th\ derivative\ of\ function\ xarccos(-2)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( xarccos(-2)\right)}{dx}\\=&arccos(-2) + x(\frac{-(0)}{((1 - (-2)^{2})^{\frac{1}{2}})})\\=&arccos(-2)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( arccos(-2)\right)}{dx}\\=&(\frac{-(0)}{((1 - (-2)^{2})^{\frac{1}{2}})})\\=&0\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\ \end{split}\end{equation} \]
>>注：本次最多计算 7 道题。
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/7]Find\ the\ 4th\ derivative\ of\ function\ \frac{x}{}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[2/7]Find\ the\ 4th\ derivative\ of\ function\ xsqrt(-1)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( xsqrt(-1)\right)}{dx}\\=&sqrt(-1) + x*0*\frac{1}{2}*-1^{\frac{1}{2}}\\=&sqrt(-1)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( sqrt(-1)\right)}{dx}\\=&0*\frac{1}{2}*-1^{\frac{1}{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[3/7]Find\ the\ 4th\ derivative\ of\ function\ xln(0)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( xln(0)\right)}{dx}\\=&ln(0) + \frac{x*0}{(0)}\\=&ln(0)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( ln(0)\right)}{dx}\\=&\frac{0}{(0)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[4/7]Find\ the\ 4th\ derivative\ of\ function\ xtan(90)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( xtan(90)\right)}{dx}\\=&tan(90) + xsec^{2}(90)(0)\\=&tan(90)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( tan(90)\right)}{dx}\\=&sec^{2}(90)(0)\\=&0\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[5/7]Find\ the\ 4th\ derivative\ of\ function\ x{0}^{-2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{0}x\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{0}x\right)}{dx}\\=&\frac{1}{0}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{1}{0}\right)}{dx}\\=&0\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[6/7]Find\ the\ 4th\ derivative\ of\ function\ xarcsin(2)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( xarcsin(2)\right)}{dx}\\=&arcsin(2) + x(\frac{(0)}{((1 - (2)^{2})^{\frac{1}{2}})})\\=&arcsin(2)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( arcsin(2)\right)}{dx}\\=&(\frac{(0)}{((1 - (2)^{2})^{\frac{1}{2}})})\\=&0\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[7/7]Find\ the\ 4th\ derivative\ of\ function\ xarccos(-2)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( xarccos(-2)\right)}{dx}\\=&arccos(-2) + x(\frac{-(0)}{((1 - (-2)^{2})^{\frac{1}{2}})})\\=&arccos(-2)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( arccos(-2)\right)}{dx}\\=&(\frac{-(0)}{((1 - (-2)^{2})^{\frac{1}{2}})})\\=&0\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\ \end{split}\end{equation} \]
>>注：本次最多计算 7 道题。